How do you differentiate # f(x) =2xcos x #?

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Answer 1 · 2016-01-24T23:47:22

#f'(x)=2(cosx-xsinx)#

Use the product rule, which states that the derivative of a product of functions, like #f(x)=g(x)h(x)#, is

#f'(x)=g'(x)h(x)+g(x)h'(x)#

Here, we have

#g(x)=2x#
#h(x)=cosx#

The derivatives of each of these are

#g'(x)=2#
#h'(x)=-sinx#

Plug these both back in to find #f'(x)#.

#f'(x)=2(cosx)+2x(-sinx)#

Which can be simplified to be

#f'(x)=2(cosx-xsinx)#